Talk:Component (graph theory)

Merger proposal
User:DPoon has suggested that strongly connected component be merged here. I strongly disagree. We could perhaps use an article that would survey various notions of components in graph theory (connected components and biconnected components of undirected graphs, strongly connected components of directed graphs, etc) but both connected components and strongly connected components deserve their own articles: they are fundamental, important, have plenty of algorithmic depth, etc. And while connected components are reasonably intuitive and natural, strongly connected components require more care to define and use; including that material here would necessarily make it shorter and harder to understand while also confusing readers who only care about the undirected case. —David Eppstein (talk) 20:01, 1 October 2008 (UTC)

Start Class
This article is definitely not a stub so I have upgraded it to start. I am not sure if it meets the criteria for C-class so left it at that. Acb314 (talk) 11:38, 14 August 2009 (UTC)

connected components for directed graphs
According to this articles definition:
 * [A] connected component of an undirected graph is a subgraph in which any two vertices are connected to each other by paths, and to which no more vertices or edges (from the larger graph) can be added while preserving its connectivity

I'm looking for the name you can give to a "connected component" of a directed graph. That is, I'm looking for XYZ, for which the following definition holds:
 * A XYZ of an directed graph is a subgraph in which for any two vertices v1, v2 in this subgraph there is a path from v1 to v2 or there is a path from v1 to v2, and to which (subgraph) no more vertices or edges (from the larger graph) can be added while preserving its connectivity.

It should be called something like "maximally connected subgraph of a directed graph", though I guess there is already a special name for it. Thanks, --Abdull (talk) 21:50, 2 August 2010 (UTC)
 * I'm not sure that's the definition you really want. For instance, consider a graph with k layers, and n/k vertices per layer, with an edge between every two vertices on consecutive layers (directed from the higher layer to the lower one) — then there are (n/k)k different subgraphs formed by a path from the top layer to the bottom one, each of these subgraphs fits your description, and they don't form any kind of nice partition of the graph. But instead, if you require that there is both a path from v1 to v2 and a path from v2 to v1, then you do get a nice partition of the vertices into strongly connected components. —David Eppstein (talk) 21:59, 2 August 2010 (UTC)
 * Thank you for your fast reply (9 minutes! :). Though I didn't understand it yet, as I don't know the definition of layer. There is neither a Wikipedia article on it, nor is there an entry about it in the glossary of graph theory. Can you give a definition or point to one? Cheers, --Abdull (talk) 18:12, 3 August 2010 (UTC)
 * I didn't mean it in any standard formal sense, just as a way of identifying subsets of vertices. Define a collection of disjoint subsets of vertices, call them "layers", order them into a sequence, and put a directed edge between two vertices if they are in two layers that are consecutive in the ordering. —David Eppstein (talk) 18:17, 3 August 2010 (UTC)

Union-find-delete
The Algorithms section talks about amortized O(|V|) deletion of edges in disjoint-set data structure. Amortized constant time per edge delete can be achieved in disjoint-set while still maintaning the same time complexity of the other operations. Construction of such a data structure is described in several papers, that can be easily found using "union find delete" query in any search engine (Google being probably the best one). I am not familiar with Wikipedia's policies and I don't feel confident to change this article as I am just an undergrad student of computer science. 78.128.196.3 (talk) 09:05, 27 April 2013 (UTC)

Rename article to Component (graph theory), and refer to all "Connected components" and just components throughout the article.
A component, by definition is a connected subgraph of a graph, the term connected component is redundant, and does not appear in most texts.

The term "connected component" does however appear a lot in computer science literature, from what I've seen online. However, this is more of a math article than it is a compsci one, so I would argue the definition and use of the term seen most in Graph Theory texts would be more suitable. — Preceding unsigned comment added by Zer0dept (talk • contribs) 22:16, 17 March 2019 (UTC)